In this work we generate the numerical solutions of Burgers’ equation by applying the Crank-Nicholson method and different schemes for solving nonlinear systems, instead of using Hopf-Cole transformation to reduce Burgers’ equation into the linear heat equation. The method is analyzed on two test problems in order to check its efficiency on different kinds of initial conditions. Numerical solut...

In this paper, we present a novel second order in time mixed finite element scheme for the Cahn-Hilliard-Navier-Stokes equations with matched densities. The scheme combines a standard second order Crank-Nicholson method for the Navier-Stokes equations and a modification to the Crank-Nicholson method for the Cahn-Hilliard equation. In particular, a second order Adams-Bashforth extrapolation and ...

Sickle cell disease (SCD) is a genetic disorder that alters the red blood cell (RBC) structure and function such that hemoglobin (Hb) cannot effectively bind and release oxygen. Our novel 2-D computational model represents a fast, time efficient method developed to analyze flow dynamics, O2 diffusion, and cell deformation in the microcirculation. A finite difference, Crank-Nicholson scheme is u...

In this paper, in an arbitrary Hilbert space nonlocal boundary value problem for the Schrödinger equation with time dependent self-adjoint operator is studied. Stability estimates solution of established. To find approximate first order accuracy Rothe difference scheme and second Crank-Nicholson are constructed. these schemes have been obtained. obtain stability estimates, theory spectral repre...

Britain?Achievements and Problems. By J. H. Nicholson. (Report sponsored by the Carnegie United Kingdom Trust and the National Council of Social Service and published by the N.C.S.S.) This report attempts to review the social consequences of rehousing policies in the country as a whole and covers not only the new towns, but also selected housing estates and expanded towns. Dr. Nicholson found m...